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Approximation Problem


The approximation problem is a well known problem of functional analysis (Grothendieck 1955). It asks to determine whether every compact operator T from a Banach space X to a Banach space Y is the uniform operator topology of a sequence of operators with finite rank. This question was answered in the negative by Enflo (1973), who provided a deep counterexample to this problem.


See also

Approximation Property, Banach Space, Compact Operator

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References

Enflo, P. "A Counterexample to the Approximation Problem in Banach Spaces." Acta Math. 130, 309-317, 1973.Grothendieck, A. Produits tensoriels topologiques et espaces nucléaires. Providence, RI: Amer. Math. Soc., 1955.

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Approximation Problem

Cite this as:

Weisstein, Eric W. "Approximation Problem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ApproximationProblem.html

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